Numerical simulation of dynamic behaviour of internal transport with a barrier trigger in Tokamak plasmas in splitting domain and its parallel computation are shown.The parallel efficiency increases with the computing scale.Numerical results agree well with theoretical analysis.The code adapts to the simulation of nonlinear tearing mode (specially mutiple mode) as well.

The strong dependence of fusion reaction rate on ion temperature leads to a thermalinstability of D T burning plasma.Mathematical qualites are discussed for the non-linear differential equations describing the steady state power balance of a D T burning plasma.Shooting method is used to obtain equilibrium solution and eigenvalue of the linearized equation about temperature pertubation around equilibrium.How ever,the solution obtained by the above method can be different from the time-dependent one for t→∞.This provides a typical example of a kind of unsolved non-linear mathematical problem.

The eigenvalue problem of the secular trapped ion temperature gradient mode is solved by employing invariant imbedding method. The numerical methods removing the singularity of the eigen equation at zero point are presented for even mode and odd mode, respectively. The calculation for a concrete physical problem is outlined.

Numerical method of the steady-state Fokker-planck equation is discussed.The numerical results are obtained by linear combination method and single step method based on Gauss node collection. Ratio frequency(RF) current density and power density of the steady state low hybrid wave(LHW) current drive are calculated numerically.